Typically, a solid oxide fuel cell (SOFC) employs a solid electrolyte of ion-conductive solid oxide such as stabilized zirconia. The solid electrolyte is interposed between an anode and a cathode to form an electrolyte electrode assembly (hereinafter also referred to as MEA). The electrolyte electrode assembly is sandwiched between separators (bipolar plates). In use, generally, predetermined numbers of the electrolyte electrode assemblies and the separators are stacked together to form a fuel cell stack.
As a system including this type of fuel cell stack, for example, a fuel cell battery disclosed in Japanese Laid-Open Patent Publication No. 2001-236980 (hereinafter referred to as the conventional technique 1) is known. As shown in FIG. 8, the fuel cell battery includes a fuel cell stack 1a, and a heat insulating sleeve 2a is provided at one end of the fuel cell stack 1a. A reaction device 4a is provided in the heat insulating sleeve 2a. The reaction device 4a includes a heat exchanger 3a. 
In the reaction device 4a, as a treatment of liquid fuel, partial oxidation reforming which does not use water is performed. After the liquid fuel is evaporated by an exhaust gas, the liquid fuel passes through a feeding point 5a which is part of the heat exchanger 3a. The fuel contacts an oxygen carrier gas heated by the exhaust gas thereby to induce partial oxidation reforming, and then, the fuel is supplied to the fuel cell stack 1a. 
Further, as shown in FIG. 9, a solid oxide fuel cell disclosed in Japanese Laid-Open Patent Publication No. 2010-504607 (PCT) (hereinafter referred to as the conventional technique 2) has a heat exchanger 2b including a cell core 1b. The heat exchanger 2b heats the cathode air utilizing waste heat.
Further, as shown in FIG. 10, a fuel cell system disclosed in Japanese Laid-Open Patent Publication No. 2004-288434 (hereinafter referred to as the conventional technique 3) includes a first area 1c having a circular cylindrical shape extending vertically, and an annular second area 2c around the first area 1c, an annular third area 3c around the second area 2c, and an annular fourth area 4c around the third area 3c. 
A burner 5c is provided in the first area 1c, and a reforming pipe 6c is provided in the second area 2c. A water evaporator 7c is provided in the third area 3c, and a CO shift converter 8c is provided in the fourth area 4c. 